NCERT Solutions: Data Handling and Presentation

Table of Contents
1. Page 75
2. Page 76
3. Page 77
4. Page 78
5. Page 83 & 84
6. Page 86
7. Page 88
8. Page 93 & 94
9. Page 95
10. Page 96
11. Page 97
12. Page 98
13. Page 99 & 100
14. Page 103
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Page 75

Naresh and Navya decided to go to each student in the class and ask what their favourite game is. Then they prepared a list. 
Navya is showing the list:

She says (happily), "I have collected the data. I can figure out the most popular game now!"

A few other children are looking at the list and wondering, "We can't yet see the most popular game. How can we get it from this list?"

Ans: Based on the data, here is how the favourite games of the students are distributed:

• Kabaddi: 6 students (Mehnoor, Simran, Ankita, Anaya, Arsh, Sarah)
• Hockey: 8 students (Jubimon, Leela, Afshan, Imon, Rehana, Gurpreet, Navjot, Ananya)
• Satoliya (Pittu): 5 students (Nand, Pushkal, Jivika, Jivisha, Hemal)
• Cricket: 6 students (Yuvraj, Keerat, Soumya, Bhavya, Tahira, Hardik)
• Football: 4 students (Rajesh, Thara, Kompal, Debabrata)
• Badminton: 2 students (Densy, Aarna)

Most Popular Game: Hockey is the most popular game, with 8 students choosing it. This is found by counting how many students chose each game and comparing the counts.

Figure it Out

Q1: What would you do to find the most popular game among Naresh's and Navya's classmates?
Ans: To find the most popular game, organise the raw data first. You can use tally marks to count each time a game is mentioned, then draw a pictograph or a bar graph to compare the counts visually. The game with the highest count is the most popular.

Q2: What is the most popular game in their class?
Ans: The most popular game in their class is Hockey, because it has the highest frequency (8 students).

Q3: Try to find out the most popular game among your classmates.
Ans: Cricket is the most popular game among our classmates. (This answer will vary by class; students should collect and count the responses to confirm.)

Q4: Pari wants to respond to the questions given below. Put a tick (✔) for the questions where she needs to carry out data collection and put a cross (✘) for the questions where she doesn't need to collect data. Discuss your answers in the classroom.

(a) What is the most popular TV show among her classmates?
Ans: ✔ (You must collect each classmate's preference and count to find the most popular show.)

(b) When did India get independence?
Ans: ✘ (This is a known historical fact and does not require local data collection.)

(c) How much water is getting wasted in her locality?
Ans: ✔ (You need to measure or survey households to estimate the amount of water wasted.)

(d) What is the capital of India?
Ans: ✘ (This is a factual question with a fixed answer and does not require data collection.)

Page 76

Figure it Out

Q1: Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:

• How many students chose jalebi? _______
  Ans: 6 students chose jalebi. 
• Barfi was chosen by_______ students?
  Ans: Barfi was chosen by 3 students.
• How many students chose gujiya?_______
  Ans: Gujiya was chosen by 13 students.
• Rasgulla was chosen by _______ students?
  Ans: Rasgulla was chosen by 7 students.
• How many students chose gulab jamun?_______
  Ans: Gulab jamun was chosen by 9 students.

Shri Nilesh requested one of the staff members to bring the sweets as given in the table. The table helped him purchase the correct number of sweets for each flavour.

Q2: Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?
Ans: No. The table shows only how many students like each sweet; it does not link each student to the sweet they prefer. To give each student the correct sweet, you need raw data that records each student's choice by name. An alternative is a list that pairs each student's name with their chosen sweet or a labelled card for each student.

Page 77

She then arranged the shoe sizes of the students in ascending order-

Figure it Out

Q1: Help her to figure out the following -

• The largest shoe size in the class is _________.
  Ans: The largest shoe size in the class is 7.
• The smallest shoe size in the class is _________.
  Ans: The smallest shoe size in the class is 3.
• There are _________ students who wear shoe size 5.
  Ans: There are 10 students who wear shoe size 5.
• There are _________ students who wear shoe sizes larger than 4.
  Ans: There are 15 students who wear shoe sizes larger than 4.

Q2: How did arranging the data in ascending order help to answer these questions?
Ans: Arranging the data in ascending order makes it easy to spot the smallest and largest values and to count how many times each size appears. This organised view reduces the chance of missing any sizes when counting.

Q3: Are there other ways to arrange the data?
Ans: Yes. You can arrange the data in descending order (largest to smallest), or group it by frequency to make a frequency table showing how many students wear each size. Both methods also help in analysis.

Page 78

Q4: Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table -

(a) Which tree was found in the greatest number?
(b) Which tree was found in the smallest number?
(c) Were there any two trees found in the same numbers?

Ans:

(a) Mango tree.
(b) Peepal tree.
(c) No, there were no two trees found in the same number. (This answer follows from counting each tree type on the route and comparing totals.)

Q5: Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters 'c', 'e', 'i', 'r', and 'x' in the words of the news article, and fill in the table.

(a) The letter found the most number of times is ________.
(b) The letter found the least number of times is ________.
(c) List the five letters 'c', 'e', 'i', 'r', 'x' in ascending order of frequency. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order 'x, c, r, i, e'.) Why do you think this is the case?
(d) Write the process you followed to complete this task.
(e) Discuss with your friends the processes they followed.
(f) If you do this task with another news item, what process would you follow?

Ans:

(a) The letter is 'a'.
(b) The letter is 'x'.
(c) Letters in ascending order : x, c, r, i, e. 
Yes, my order is nearly the same as others because common letters such as 'e' and 'i' occur more frequently in English words while 'x' is much rarer. This reflects typical letter frequency in English.

(d) I made tally marks for each of the given letters as I read the article, then counted the tallies to get the totals.
(e) To be done by the students.
(f) I would follow the same process: read the article, mark tallies for each occurrence of the letters, then total the counts and order them by frequency.

Page 83 & 84

Figure it Out

Q1: The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori:

(a) On which day were the minimum number of books borrowed?
Ans: Thursday. 

(b) What was the total number of books borrowed during the week?
Ans: Total number of books borrowed = 5 + 4 + 2 + 0 + 5 + 8 = 24 books. Add the counts for each day to get the weekly total.

(c) On which day were the maximum number of books borrowed? What may be the possible reason?
Ans: Saturday had the maximum borrowing (8 books). A likely reason is that students have more free time on Saturdays and may visit the library to borrow books for the weekend.

Q2: Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold to these six shopkeepers are given below:

Prepare a pictograph using the symbolto represent 100 kites. Answer the following questions:
(a) How many symbols represent the kites that Rani purchased?
(b) Who purchased the maximum number of kites?
(c) Who purchased more kites, Jasmeet or Chaman?
(d) Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?

Ans:

(a) 3 symbols represent the kites that Rani purchased. (Each symbol = 100 kites, so 3 symbols = 300 kites.)
(b) Poonam Ben purchased the maximum number of kites.
(c) Jasmeet purchased more kites than Chaman.
(d) Yes. Rani purchased 300 kites, so double that is 600 kites. Poonam Ben purchased 700 kites, which is more than 600, so Rukhsana is correct. Calculation: Double of 300 = 2 × 300 = 600; 700 > 600.

Page 86

Answer the following questions using the bar graph:

Q1: In Class 2, ___________ students were absent that day.

Ans: In Class 2, 5 students were absent that day.

Q2: In which class were the maximum number of students absent? ___________

Ans: The maximum number of students were absent in Class 8. (Absent Students = 7)

Q3: Which class had full attendance that day? ___________

Ans: Class 5 had full attendance that day.

Page 88

Figure it Out

Q1: How many total cars passed through the crossing between 6 am and noon?

Ans: Total cars = 150 + 1200 + 1000 + 800 + 700 + 600 = 4,450 cars.

Q2: Why do you think so little traffic occurred during the hour of 6-7 am, as compared to the other hours from 7 am to noon?
Ans: Most people begin their daily activities later than 6 am. Shops, offices and schools usually open after 7-8 am, so fewer vehicles are on the road between 6-7 am.

Q3: Why do you think the traffic was the heaviest between 7 am and 8 am?
Ans: Many people commute to work or school around 7-8 am, causing a peak in traffic during that hour.

Q4: Why do you think the traffic was lesser and lesser each hour after 8 am all the way until noon?
Ans: As commuters reach their destinations by about 8-9 am, fewer vehicles remain on the road, so traffic gradually decreases towards noon.

Page 93 & 94

Use the bar graph to answer the following questions: 
Q1: On which item does Imran's family spend the most and the second most? 

Ans: Imran's family spends the most on food. The second largest expense is house rent. 

Q2: Is the cost of electricity about one-half the cost of education? 
Ans: Yes. Electricity costs ₹400 while education costs ₹800, so electricity is exactly one-half of the education expense.

Q3: Is the cost of education less than one-fourth the cost of food?
Ans: No. One-fourth of food cost (₹3,400) is ₹850. Education costs ₹800, which is slightly less than ₹850 but not less than one-fourth; it is just under one-fourth of food cost.

Figure it Out

Q1: Samantha visited a tea garden and collected data of the insects and critters she saw there. Here is the data she collected:

Help her prepare a bar graph representing this data.
Ans:

(Use the given counts and draw vertical bars for each insect type with a suitable scale on the vertical axis.)
Q2: Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a 2-hour period.

She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.

(a) Write the number of tickets sold for Vidisha above the bar.
Ans: The number of tickets sold for Vidisha is 24.

(b) Write the number of tickets sold for Jabalpur above the bar.
Ans: The number of tickets sold for Jabalpur is 20.

(c) The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?
Ans: For Vidisha, 
6 unit bar length = 24 tickets 
1 unit bar length = 24/6 
1 unit bar length = 4 tickets. 
For Jabalpur, 
5 unit bar length = 20 tickets 
1 unit bar length = 20/5 
1 unit bar length = 4 tickets.
Therefore, Scale for this graph: 1 unit length = 4 tickets

(d) Draw the correct bar for Sagar.
Ans:

(e) Add the scale of the bar graph, placing the correct numbers on the vertical axis.
Ans: The scale on the vertical axis should show multiples of 4: 4, 8, 12, 16, 20, 24, etc., matching the unit length = 4 tickets used for the bars.

(f) Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
Ans: No, the bars for Seoni and Indore are not correct in the given graph. They should be redrawn so their heights match their ticket numbers using the scale 1 unit = 4 tickets; the corrected bars are shown in the updated graph above.

Q3: Chinu listed the various means of transport that passed across the road in front of his house from 9 AM to 10 AM:

(a) Prepare a frequency distribution table for the data.
Ans:

(b) Which means of transport was used the most?
Ans: Bike was used the most. 

(c) If you were there to collect this data, how could you do it? Write the steps or process.
Ans: If I were collecting the data, I would:

• Create a table with columns for the means of transport and for tally marks.
• As each vehicle passes, mark a tally in the correct row.
• After one hour, count the tallies to get the frequency for each transport type.
• Record the totals in the frequency column and check for mistakes by recounting if needed.

Page 95

Q4: Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared:
(a) The minimum number of times.
(b) The maximum number of times.
(c) Find numbers that appeared an equal number of times.

Ans: Let the outcomes of 30 rolls of a die be:
6, 2, 3, 5, 6, 4, 1, 1, 2, 5
3, 4, 1, 1, 3, 5, 2, 2, 1, 1
6, 2, 3, 5, 1, 2, 2, 3, 4, 2

(a) 4 and 6 appeared the minimum number of times.
(b) 2 appeared the maximum number of times.
(c) 4 and 6 appeared an equal number of times. 

Q5: Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:

(a) What information is this table giving?
Ans: The table shows how many matches Bumrah took each possible number of wickets (from 0 to 7), listing the frequency of matches for each wicket count.

(b) What may be the title of this table?
Ans: Frequency distribution of wickets taken by Jaspreet Bumrah in his last 30 matches.

(c) What caught your attention in this table?
Ans: It is noticeable that Bumrah took 3 or more wickets in most matches, showing a strong bowling performance overall.

(d) In how many matches has Bumrah taken 4 wickets?
Ans: He took 4 wickets in 3 matches. 

(e) Mayank says "If we want to know the total number of wickets he has taken in his last 30 matches, we have to add the numbers 0, 1, 2, 3 ..., up to 7." Can Mayank get the total number of wickets taken in this way? Why?
Ans: No. Adding the labels 0, 1, 2, ..., 7 gives only the list of wicket counts, not the total wickets. To get the total wickets, each wicket count must be multiplied by its frequency (number of matches with that count) and then those products are added.

(f) How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?
Ans: Total wickets = 1 × 4 + 2 × 6 + 3 × 8 + 4 × 3 + 5 × 5 + 6 × 1 + 7 × 1 = 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 wickets.

Page 96

Q6: The following pictograph shows the number of tractors in five different villages.

Observe the pictograph and answer the following questions-

(a)Which village has the smallest number of tractors?

Ans: Village D has the smallest number of tractors.

(b) Which village has the most tractors?
Ans: Village C has the most tractors.

(c) How many more tractors does Village C have than Village B?
Ans: Village C has 3 more tractors than Village B.

(d) Komal says, "Village D has half the number of tractors as Village E." Is she right?
Ans: Yes. Village D has 3 tractors and Village E has 6 tractors, so Village D has exactly half the number of tractors of Village E.

Page 97

Q7: The number of girl students in each class of a school is depicted by a pictograph:

(a) Which class has the least number of girl students?
Ans: Class 8 has the least number of girl students. 

(b) What is the difference between the number of girls in Class 5 and 6?
Ans: Number of girls in Class 6 = 4 × 4 = 16.
Number of girls in Class 5 = 4 × 2.5 = 10.
Hence difference = 16 - 10 = 6 girls.

(c) If 2 more girls were admitted in Class 2, how would the graph change?
Ans: The graph will have 5 full symbols of girls.

(d) How many girls are there in Class 7?
Ans: Girls in Class 7 = 3 × 4 = 12.

Page 98

Q8: Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka's Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows:
Village A : 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F : 24
Prepare a pictograph and answer the following questions:

(a) What will be a useful scale or key to draw this pictograph?
Ans: A useful key is: one symbol represents 6 dogs. This gives integer symbol counts for all villages.

(b) How many symbols will you use to represent the dogs in Village B?
Ans: Village B has 36 dogs. With one symbol = 6 dogs, use 36/6 = 6 symbols to represent Village B.

(c) Kamini said that the number of dogs in Village B and Village D together will be more than the number of dogs in the other 4 villages. Is she right? Give reasons for your response.
Ans: Yes. Village B + Village D = 36 + 48 = 84 dogs. The other four villages total = 18 + 12 + 18 + 24 = 72 dogs. Since 84 > 72, Kamini is correct.

Q9: A survey of 120 school students was conducted to find out which activity they preferred to do in their free time.

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?
Ans:

Most students prefer reading story books other than playing. 

Page 99 & 100

Q10: Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows:

(a) The total number of saplings planted on Wednesday and Thursday is ___________.
Ans: Total saplings planted on Wednesday and Thursday = 30 + 40 = 70 saplings.

(b) The total number of saplings planted during the whole week is ___________.
Ans: Total saplings planted during the whole week = 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312 saplings.

(c) The greatest number of saplings were planted on ___________, and the least number of saplings were planted on ___________.
Ans: The greatest number of saplings were planted on Saturday, and the least number of saplings were planted on Wednesday. 
At the beginning of the week (Monday), People might have higher energy levels, resulting in more saplings being planted. 
But as the week progresses, people may get fatigued due to work or other activities, resulting in fewer plantation of saplings. 
By Friday and Saturday, people might be more willing to go outdoors and engage in activities like plantation. 
The decline in the plantation of saplings on Sunday might be due to exhaustion after the weekend.

Q11: The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in 4-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?

Ans: Yes, there are mistakes in the graph. The corrected bar graph should show the following accurate values:

• No. of tigers in 2006 was 1,400 but shown less in the graph.
• No. of tigers in 2014 was 2,200 but shown more in the graph.
• No. of tigers in 2018 was 3,000 but shown less in the graph.

Page 103

Figure it Out

Q1: If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?
Ans: I would use vertical bars because height is a measure that is naturally shown by upward length; vertical bars make it easy to compare heights directly.

Q2: If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar graph with vertical bars or with horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest rivers?
Ans: I would prefer horizontal bars for river lengths because distances run left-right along the page and long names fit more easily beside horizontal bars. After collecting river-length data for each continent, plot horizontal bars with a suitable scale to compare lengths. Continents with the longest rivers include Africa (Nile) and South America (Amazon).